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Unrestricted geometric distance functions and the Geometric Young productivity index: an analysis of Indian manufacturing

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Abstract

In this paper, we employ the less frequently used Geometric Young index to measure productivity change. We reformulate the Geometric Distance Function of Portela and Thanassoulis (J Product Anal 25:25–41, 2006) by removing the restrictions on the individual input scaling factors and the output scaling factors to obtain the benchmark input–output bundle on the frontier. In this reformulated model, the Geometric Young index is exhaustively decomposed into the technical efficiency change and technical change factors even under variable returns to scale. Further, between any two periods, the measured rate of technical change is identical across all units. In our empirical analysis, we use state-level data from the Annual Survey of Industries for the period 2010–2011 through 2016–2017 to measure total factor productivity growth in Indian manufacturing and provide its decomposition for the major manufacturing states in India. At the All-India level, the annual average Geometric Young productivity index shows a modest growth over the sample period. This resulted from an improvement in technical efficiency reinforced by a very modest increase in the Technical Change Index.

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Notes

  1. For a detailed discussion of Index Numbers, see the survey by Rao (2020).

  2. The data are reported by accounting year which runs from April 1 to March 31. For example, the year 2016–2017 refers to the period April 1, 2016, to March 31, 2017. Henceforth, for simplicity we will refer to it as year 2016 and similarly for the other years in our sample.

  3. For an application of the Lowe productivity index and its decomposition, see O’Donnell (2012).

  4. Use of the notation t and t + 1 to denote adjacent periods is the generalization of the notation 0 and 1 used in previous discussion.

  5. They recognize, though, that ‘the GDF in (4) used to calculate TFP is not an efficiency measure as it does not account for distances between observed and target levels but between two points observed in two time periods’ (PT 2006, p. 30).

  6. In PT (2006), there is no explicit restriction on the input and output scaling factors. In fact, they do not algebraically formulate the production possibility set empirically constructed from the data. But as shown in this paper, the residual component (which they describe as ‘scale-related’) will equal unity even under VRS unless the inputs scaling factors are restricted from above and output scaling factors are restricted from below at 1. In another paper PT (2007), they explicitly impose these restrictions in Eq. (3) where they measure technical efficiency. Later, in the same paper, for the standard profit maximization problem (4) (PT 2007, p 483), they remove these restrictions. But that is unrelated to the GDF.

  7. This result was first presented in a preliminary form in Ray and Chen (2009) and later in Ray and Chen (2014). More recently, Aparicio et al. (2017) derive a decomposition of the Geometric Young index without the residual scale factor (although they describe this as a geometric mean of partial Malmquist productivity changes). However, they assume CRS (see their slide 7) which automatically rules out the scale factor.

  8. In our empirical analysis, we applied this iterative process. In most cases, the optimal solution converged at the second iteration. Only in a very few cases, convergence took place at the third or fourth iteration.

  9. The importance of other factors in determining productivity growth and performance has also been highlighted in the literature. For example, Aghion et al. (2008) and Veermani and Goldar (2004) emphasize that states with better investment climate experienced higher productivity growth in Indian manufacturing during the post-reform years.

  10. As mentioned previously, this refers to the accounting years 2010–2011 to 2016–2017.

  11. The corresponding percentages for these eight states were 71%, 73%, and 71% in 2011. The drop in percentage share between 2011 and 2016 could be partly due to the fact that in 2014 there was a geographic reorganization of the states and the state of Andhra Pradesh (AP) was broken up into two states—Andhra Pradesh (AP) and Telangana (TE).

  12. It may be noted that in manufacturing the material input typically accounts for an overwhelmingly large share of production cost. For example, in the year 2007 for the U.S. states the average share was 67%, varying between 51% for Connecticut (CT) and 79% for Delaware (DE).

  13. We thank an anonymous referee for this suggestion.

  14. Here, labor productivity is measured by output per person employed, without distinguishing between production and non-production workers.

  15. In this single-output case, the output index is simply the ratio of real values of gross outputs in consecutive years.

  16. Note that Table 5 does not report the decomposition for ‘All India.’ This is because our decision-making units are the ‘typical factory’ in each of the 26 states. The typical factory in ‘All India’ is not included as an individual unit. However, from the annual Geometric Young productivity index reported in Table 4 and given the annual Technical Change Index in Table 5, which is uniform across all units, we can impute the Technical Efficiency Change Index for the typical factory at the All-India level.

  17. Although in our empirical analysis, the cost shares remained very stable over our sample period, this may not always be true if there are shocks that cause these shares to fluctuate over the sample period. Given the crucial role of these reference weights in using the Geometric Young productivity index, it may be a worthwhile practice in general to utilize alternative sets of reference weights to check for robustness of results.

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Acknowledgements

The authors thank two anonymous referees and the editors for valuable comments on an earlier version of the manuscript. The usual disclaimer applies.

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Authors and Affiliations

  1. University of Connecticut, Storrs, CT, 06269-1063, USA

    Subhash C. Ray

  2. International Management Institute New Delhi, New Delhi, India

    Arnab K. Deb

  3. Babson College, Babson Park, MA, 02457, USA

    Kankana Mukherjee

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  1. Subhash C. Ray
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Ray, S.C., Deb, A.K. & Mukherjee, K. Unrestricted geometric distance functions and the Geometric Young productivity index: an analysis of Indian manufacturing. Empir Econ 60, 3103–3134 (2021). https://doi.org/10.1007/s00181-020-01925-0

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